As has already been pointed out in British Specification No. 1,401,042 quartz crystals of frequencies greater than 1 MHz have generally tended to be of a circular lens form and such forms suffer from various disadvantages including, of course, the problem of space occupation and the difficulty of manufacture including mounting. Accordingly, it was concluded that a rectangular form of quartz crystal would be much preferable, particularly where it was desired to use such a quartz as a resonator in a wrist watch. In such application the quartz resonator is subject to many problems not found in other applications. For example in view of a large variation of temperature it may be found necessary to provide arrangements for bringing about compensations and in any event it is desirable to provide a resonator having as flat a temperature characteristic as possible. Such resonator should likewise provide high dynamic capacitance. In view of the severe stresses which such a crystal must constantly undergo the mounting arrangements must be perfectly secure and must not in any way influence the frequency of the crystal. Thus, it has been proposed that where a high frequency quartz is to be used that such be of the AT-type in which, of course, as is well known principal vibrations occur in thickness shear. In order to deal with the quartz mounting problem, as pointed out in the British specification referred to hereinabove, an energy trapping arrangement may be provided whereby the ends of the rectangular bar are practically free of vibration and thus do not, in fact, influence the frequency of the portion of the crystal located between the electrodes.
Various problems remain however in respect of the earlier specification which derive from coupled flexural vibrations which tend to disturb the Q-factor. If we assume a rectangular AT-cut bar of quartz having length X, thickness Y and width Z it will be found that XY shear vibrations are always coupled to XY flexural vibrations. For ratios X/Y of high value, for example 30 or greater, regions will be found where the shear vibrations clearly dominate the flexural vibrations. The characteric curves will show a horizontal portion or shelf where the frequency of the vibrating plate will be neighbouring that which would correspond to pure shear at the same time remaining slightly higher.
For low ratios of length to thickness this shelf no longer exists and one passes imperceptibly from zones where flexural vibrations dominate to those where shear dominates. The technique of energy trapping which tends to limit the shear energy within a limited portion of the plate does not act on the flexural mode which may propagate freely along the length. Thus, mounting the resonator at its ends when such resonator has its long dimension according to X may be extremely critical since it is always necessary to find points where the vibration amplitude is zero. If however one should choose to use the Z' rotated axis as the long axis of the plate there will not be the same mounting problems since the flexural vibrations end up on the free faces of the resonator. Considerable work has been done on the problem of coupling between thickness shear and flexural vibrations in crystal plates, see for example the paper published by Raymond D. Mindlin in the Journal of Applied Physics, Vol. 22, No. 3, March 1951. This paper provides the first theoretical approach for the calculation of resonator frequencies of a rectangular plate taking into account flexure and shear vibrations in respect of the elastic constants of the material.
The present invention goes a step further in providing an arrangement which takes into account temperature variations which affect the elastic constants, thereby modifying the thermal frequency coefficients.
In the U.S. Pat. No. 2,306,909 to Sykes, resonators have been described having their greatest dimension parallel to the Z' axis in respect of an AT-cut type of resonator. Such resonators were almost square in form as shown in FIGS. 10 and 11 of the aforementioned patent. No mention therein was made of the energy trapping technique. Furthermore, to the best of our knowledge up to the present time very little has been known concerning the influence of the (X)-(Y) ratio on the thermal coefficient of frequency, on the dynamic capacitance and on energy trapping when the ratio (X)-(Y) has a value substantially less than 30, for example 3 - 8.
Thus, the purpose of the invention is to provide a quartz resonator having such a selection of dimensional ratios length-to-width-to-thickness as will result in rectangular form resonators of very small width and employing the energy trapping principle, this latter being obtained either by an extra thickness of metallization or a thinning down of the outer extremities of the resonator through chemical attack, ion milling, etc. and for which the greatest dimensions will be found along the axis Z' , these ratios permitting the mastery of the behaviour in temperature variations, the obtaining of a dynamic capacity of maximum value, a high quality factor and a minimization of tolerance effects during manufacturing.